The Knights (5-2, 3-0 Conference USA) forced three Memphis turnovers, including a fumble on the UCF 1-yard line in the first quarter.
Murray, starting for the first time since the season opener, had 23 carries and scored twice early. He followed a 1-yard run with an 83-yard romp that was the second-longest run from scrimmage in school history.
Bouye had another big play when he recovered a fumble and ran 79 yards for a 28-10 UCF lead.
The Tigers rushed for a season-high 240 yards behind a career-best 88 yards by Jan Steib.
Linebacker Myles Jack, who suffered a season-ending knee injury, said Thursday he decided to leave UCLA and enter the 2016 NFL draft because he wants to be compensated for his skills.
Randy Edsall will coach Maryland against No. 1 Ohio State on Saturday, the school announced Thursday as rumors swirled about his job status going forward.
Tennessee chancellor Jimmy G. Cheek has issued a statement amid rumors that alleges coach Butch Jones fought and punched senior offensive lineman Mack Crowder during a fall practice session.
Rutgers receiver Leonte Carroo returned to practice Thursday after charges that he attacked a woman he used to date were dropped, and he said he was "lucky" to be playing again.
South Carolina has decided to give up Saturday's home game against No. 7 LSU because of devastating floods that have hit the state, moving the game to Baton Rouge.
Texas says longhorn steer mascot Bevo XIV has a "life-threatening condition" and won't travel to Dallas for the team's rivalry game Saturday against No. 10 Oklahoma at the Cotton Bowl.